On second thought, my real goal is to have two different mesh2's, in this case
created by Ingo's macros,  to have a perfectly smooth transition between them.
As you point out it ultimately becomes a question of splines.

Q: What is the most simplistic way to guarantee that two splines will have a
perfectly smooth transition, say one defined  A to B, and another B to C?

That is, If I have the "extra point" in a quadratic spline overlap, or the "two
extra points" in a cubic_spline overlap?  Or again, would one have to "hard
code" them as in the example of the trig functions for spheres.

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